Asking the Right Question – Einstein

Source: Quora, Sep 2016

Einstein didn’t take 7 years to find the answer to a question; instead, he took 7 years to ask the right question in the first place.

After special relativity, Einstein decided to find a way to incorporate gravity into his theory. Special relativity is all about inertial reference frames and observers traveling at constant velocities, but free-falling observers moving under the influence of gravity always accelerate, so how could he end up with a fully relativistic theory of gravity?

Answering such a question with the knowledge that he had is like trying to navigate a huge expanse of complete darkness. Somehow you’ve got to ask a series of new, important and relevant questions that are also solvable, to try to make sense of this new territory. Any question that you ask could be intractable, but more frequently they could also be irrelevant. Even if you’ve found the right question, you must still figure out how to attack the problem.

That Einstein unraveled this whole thing is nothing short of remarkable, because it must have been confusing as hell when it was first being stated. In fact, Einstein initially set aside what became ultimately the right approach for about 2 years before coming back to it and resolving his earlier confusion. Once he understood that the use of curvature tensors of the spacetime metric was the right way to go, the final answer ended up being very simple:

which basically says that the local curvature of spacetime is proportional to the energy/momentum content at that point. Framed correctly, this is pretty straightforward, and any mathematician working on Riemannian geometry, given the right way of thinking about the problem, could have come up with it. But the key point as I’ve been arguing is in the phrase in italics: you have to go from a physical picture of gravity, and draw the connection between that and something as mathematically abstract as Riemannian geometry before things start to make perfect sense.

Once you appreciate the process by which someone could have come up with this, a question like “was Einstein bad at math” becomes absolutely pointless. He wasn’t an expert at Riemannian geometry, but he was the first to see the connection between geometry and gravity, which in itself is a profound accomplishment. He then successfully learnt the material and put all of the very confusing pieces together, and published his full theory at the same time as David Hilbert, one of the preeminent mathematicians of the 20th century, who based his work on Einstein’s earlier realizations in the first place.

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